Simplify the following expression: $ n = \dfrac{-1}{5} + \dfrac{z + 9}{-10} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10}{-10}$ $ \dfrac{-1}{5} \times \dfrac{-10}{-10} = \dfrac{10}{-50} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{z + 9}{-10} \times \dfrac{5}{5} = \dfrac{5z + 45}{-50} $ Therefore $ n = \dfrac{10}{-50} + \dfrac{5z + 45}{-50} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{10 + 5z + 45}{-50} $ $n = \dfrac{5z + 55}{-50}$ Simplify the expression by dividing the numerator and denominator by -5: $n = \dfrac{-z - 11}{10}$